Your moderate muslim countrie? Indonesia, parts of the Phillipines, Morroco, Tunisia, Senegal, Egypt depending on your definition, Jordan,Turkey, some of the 'stans, the UAE, France, Michigan and a few others.

Some of these have more or less serious jihadi problems of their own, and some do practice some version of sharia. No where I would choose to live. Still, they are not so oppresive (by regional standards) that you would write them off as being hot beds of fundamentalism either.
However as to the moderates curtailing the radicals, we don't see it as much as we should, but these things come and go.
In the fifties and sixties, moderate to liberal Christianity was on the rise in the Protestant and Catholic churches. Now fundamenalism or at least conservatism seems to have the upper hand. I would also say I haven't heard conservative Christian leaders like Pat Robertson condemn the Quran burners, despite General Patreaus asking these guys to stop.Its only a fifty member church, and them doing something stupid to get attention is going to get folks killed.
FQ13 who isn't comparing Christianity with Islam, as we aren't blowing folks up. Just saying that religious leaders rarely fire on their own fringe, which is too bad, as those are voices that need to be heard in order to delegitimate the radicals.
PS a correction. The national Council of churches and the Natioal Association of Evangelicas did condemn them. Kudos.